# Solve. 0.4y + 3 > 3.6y - 5 Apply Inequality Theorem # 1: The direction of an inequality doesn't change if the same real number is added or subtracted to both sides

Add -3.6y to both sides, the direction doesn't change:

`0.4y-3.6+3> -5`

Add -3 to both sides, the direction doesn't change:

`0.4y-3.6y> -5-3`

Simplify each side:

`-3.2y>...

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Apply Inequality Theorem # 1: The direction of an inequality doesn't change if the same real number is added or subtracted to both sides

Add -3.6y to both sides, the direction doesn't change:

`0.4y-3.6+3> -5`

Add -3 to both sides, the direction doesn't change:

`0.4y-3.6y> -5-3`

Simplify each side:

`-3.2y> -8`

Apply Inequality Theorem # 2: The direction of an inequality doesn't change if both sides are multiplied or divided by the same real number.

Divide each side by 3.2, the direction doesn't change::

`-y> -8/3.2`

Apply Inequality Theorem # 3: The direction of an inequality is inverted when both sides are multiplied or divided by the same negative number.

Multiply both sides by -1, the direction changes:

`y<8/3.2`

Simplify:

`y<2.5`

Therefore this inequality is true for all values of y<2.5

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